Polygons

2010018004

Level: 
C
A rectangle-shaped land has dimensions \(5 \times 8\,\mathrm{cm}\) on a map with scale \(1:500\). The owner increased the size of his land by buying some land from his neighbor. The new land has dimensions \(7\times 9\,\mathrm{cm}\) on the map. Find the actual increase of the perimeter of the land (i.e. find the increase in the length of the fence required to enclose the whole land). Give your answer in meters.
\(30\,\mathrm{m}\)
\(15\,\mathrm{m}\)
\(40\,\mathrm{m}\)
\(60\,\mathrm{m}\)

2010018002

Level: 
B
In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon, the blue angle is the interior angle of the polygon. Suppose we consider a regular polygon with the central angle of \(30^{\circ}\), then find the measure of the interior angle of this polygon.
\(150^{\circ}\)
\(180^{\circ}\)
\(90^{\circ}\)
\(210^{\circ}\)

2010015008

Level: 
B
Consider a regular polygon with the central angle of \(15^{\circ}\). In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find the number of vertices of this polygon.
\(24\)
\( 12 \)
\( 20 \)
\( 18 \)

2010015006

Level: 
B
The figure shows a rectangular trapezium whose bases have lengths of \( 19\,\mathrm{cm} \) and \( 14\,\mathrm{cm} \), and the longer arm is \( 13\,\mathrm{cm} \) long. Calculate the sine of angle \(\alpha\).
\( \frac{12}{13} \)
\( \frac{5}{13} \)
\( 22.62^{\circ} \)
\( 67.38^{\circ} \)

2010015005

Level: 
B
Given the isosceles trapezium \( ABCD \), where \( |AB| = 12\,\mathrm{cm} \), \( |BC| = 4\,\mathrm{cm} \), \( |CD| = 16\,\mathrm{cm} \), and \( |AD| = 4\,\mathrm{cm} \), determine the measure of \( \measuredangle BCD \).
\( 60^{\circ} \)
\( 70^{\circ} \)
\( 45^{\circ} \)
\( 120^{\circ} \)